Circumference and Areas of Circumference and Areas of CirclesCircles

Lesson 11.5Lesson 11.5Geometry HonorsGeometry Honors

Objective: Know and use the Objective: Know and use the formulas for the Circumference formulas for the Circumference

and Areas of Circlesand Areas of Circles

Lesson Focus

In this lesson, the formulas for circumference and area of a circle are stated. These formulas can be understood by using facts that have been developed about areas of regular polygons.

SummaryBasic Terms

CircumferenceThe perimeter of or distance around a circle.

Area of a CircleThe area of a disk (the region inside a circle) is πr2 when the circle has radius r.

πAn irrational number that is the ratio of the circumference of a circle to its diameter.

Area of a Circle

Area, A = πr2

Circumference

Circumference, C = 2πr = πd

Pi

• Leave answers in π form unless an approximation is specified.• The exact circumference or exact area of a circle requires that π be approximated.• π is an irrational number is not the ration of two integers, as the quotient 22/7 suggests. • In the expression C/d, d is rational, C is not, and vice versa.

Practice

1. What is the ratio of the circumference to the diameter for each circle?

2. A circle has a radius of 15. What is the diameter, circumference, and area of the circle?

3. A circle has a diameter of 8. What is the radius, circumference, and area of the circle?

4. A circle has a circumference of 26π. What is the radius, diameter, and area of the circle?

5. A circle has an area of 100π. What is the radius, diameter, and circumference of the circle?

Written Exercises

Problem Set 11.5, p.448: # 2 – 16 (even) Handout: 11-5